{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SDE simulations and statistics\n",
    "\n",
    "## Contents\n",
    "   - [Brownian motion](#sec1)\n",
    "      - [Confidence interval](#sec1.2)\n",
    "      - [Hypothesis testing](#sec1.3)\n",
    "   - [Geometric Brownian motion](#sec2)\n",
    "   - [CIR process](#sec3)\n",
    "      - [Euler-Maruyama method](#sec3.1)\n",
    "      - [Parameter estimation](#sec3.2)\n",
    "      - [Change of variables](#sec3.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as scp\n",
    "import scipy.stats as ss\n",
    "import matplotlib.pyplot as plt\n",
    "from statsmodels.graphics.gofplots import qqplot\n",
    "from scipy.special import iv\n",
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1'></a>\n",
    "# Brownian motion\n",
    "\n",
    "Let us simulate some Brownian paths.    \n",
    "Remember that the (standard) Brownian motion $\\{X_t\\}_{t\\geq 0}$ is a continuous time stochastic process, that satisfies the following properties:\n",
    "- $X_{0} = 0$.\n",
    "- The increments are stationary and independent. (see **A3** for the definition)\n",
    "- It is a martingale.\n",
    "- It has continuous paths, but nowhere differentiable.\n",
    "- $X_t - X_s \\sim \\mathcal{N}(0,t-s)$ for $t\\geq s \\geq 0$.\n",
    "\n",
    "For more info see here [wiki](https://en.wikipedia.org/wiki/Brownian_motion).\n",
    "\n",
    "In our simulation, each increments is such that:\n",
    "\n",
    "$$ X_{t_i+\\Delta t} - X_{t_i} = \\Delta X_i \\sim \\mathcal{N}(\\mu \\Delta t,\\, \\sigma^2 \\Delta t). $$\n",
    "\n",
    "The process at time T is given by $X_T = \\sum_i \\Delta X_i$ and follows the distribution:\n",
    "\n",
    "$$ X_T \\sim \\mathcal{N}(\\mu T,\\, \\sigma^2 T). $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#scipy.stats uses numpy.random to generate its random numbers\n",
    "np.random.seed(seed=42)   \n",
    "\n",
    "paths=4000              # number of paths\n",
    "steps=1000             # number of time steps\n",
    "\n",
    "mu = 0.1               # drift \n",
    "sig = 0.2              # diffusion coefficient or volatility \n",
    "T = 100                \n",
    "T_vec, dt = np.linspace(0, T, steps, retstep=True)\n",
    "\n",
    "X0 = np.zeros((paths,1))        # each path starts at zero\n",
    "increments = ss.norm.rvs(loc=mu*dt, scale=np.sqrt(dt)*sig, size=(paths,steps-1))\n",
    "\n",
    "X = np.concatenate((X0,increments), axis=1).cumsum(1)\n",
    "\n",
    "plt.plot(T_vec,X.T); plt.title(\"Brownian paths\"); plt.xlabel(\"T\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we consider the terminal values of each path.  These values should give us some indications about the distribution of $X_T$.\n",
    "\n",
    "We expect to have $\\mathbb{E}[X_T] = \\mu T$ and $Std[X_T] = \\sigma \\sqrt{T}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expectation of X at time T: 9.9827\n",
      "Standard Deviation of X at time T: 1.9964\n"
     ]
    }
   ],
   "source": [
    "X_end = X[:,-1]\n",
    "print(\"Expectation of X at time T: {:.4f}\".format(X_end.mean()) )\n",
    "print(\"Standard Deviation of X at time T: {:.4f}\".format(X_end.std(ddof=1)) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I'm using the unbiased standard deviation estimator, with one degree of freedom i.e. `ddof=1`. Since the number of steps is quite big, there is no big difference between this and other possible estimators.    \n",
    "Let us recall that a common alternative is the MLE (maximum likelihood estimator), with `ddof=0`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1.2'></a>\n",
    "## Confidence intervals\n",
    "\n",
    "Ok... what we have seen so far was quite easy. Right? \n",
    "\n",
    "But... we want to be precise!  We want to associate a confidence interval to each estimated parameter!    \n",
    "In other words, we want to indicate how close the sample statistic (the estimated parameter) is to the population parameter (the real value of the parameter).\n",
    "\n",
    "We can find an interval of values that contains the real parameter, with a confidence level of $(1-\\alpha)100\\%$, for $0<\\alpha<1$. This is called **confidence interval**.\n",
    "\n",
    "Let us introduce some basic concepts:\n",
    "\n",
    "Let $X_i$ i.i.d (independent and identical distributed), for $1\\leq i \\leq n$, with $\\mathbb{E}[X_i]=\\mu$ and $Var[X_i] = \\sigma^2$.    \n",
    "We call $\\bar{X} = \\frac{1}{n}\\sum_{i=1}^n X_i$.\n",
    "- $\\bar{X}$ has expectation: $\\mathbb{E}[\\bar{X}] = \\frac{1}{n}\\sum_{i=1}^n \\mathbb{E}[X_i] = \\mu$.\n",
    "- $\\bar{X}$ has variance: $Var[\\bar{X}] = \\frac{1}{n^2} Var[\\sum_{i=1}^n X_i] = \\frac{1}{n^2} \\sum_{i=1}^n Var[X_i] = \\frac{\\sigma^2}{n}$.\n",
    "- Central limit theorem: $$ Z_n = \\frac{\\bar{X} - \\mu}{\\frac{\\sigma}{\\sqrt{n}}} \\underset{n\\to \\infty}{\\to} Z \\sim \\mathcal{N}(0,1) $$\n",
    "\n",
    "##### Normal distributed variables \n",
    "For $Z \\sim \\mathcal{N}(0,1)$, we call $z_{\\alpha/2}$ the value such that:\n",
    "\n",
    "$$ \\mathbb{P}(Z< -z_{\\alpha/2}) = \\mathbb{P}(Z > z_{\\alpha/2}) = \\alpha/2 $$\n",
    "\n",
    "Let $X_i \\sim \\mathcal{N}(\\mu,\\sigma^2)$. **Let us assume $\\sigma$ is known**.\n",
    "\n",
    "The sum of normal random variables is again normal, i.e. \n",
    "$\\sum_{i=1}^n X_i \\sim \\mathcal{N}(n\\mu,n\\sigma^2)$, therefore we have that $\\bar{X} \\sim \\mathcal{N}(\\mu,\\frac{\\sigma^2}{n})$. We can standardize and obtain $Z = \\frac{\\bar{X} - \\mu}{\\frac{\\sigma}{\\sqrt{n}}} \\sim \\mathcal{N}(0,1) $.     \n",
    "\n",
    "We can write:\n",
    "\n",
    "$$ \\begin{aligned}\n",
    "(1 - \\alpha) &= \\mathbb{P} \\biggl( -z_{\\alpha/2} < \\frac{\\bar{X} - \\mu}{\\frac{\\sigma}{\\sqrt{n}}} < z_{\\alpha/2} \\biggr) \\\\\n",
    "             &= \\mathbb{P} \\biggl(\\bar{X} - z_{\\alpha/2} \\frac{\\sigma}{\\sqrt{n}} <  \\mu < \\bar{X} + z_{\\alpha/2} \\frac{\\sigma}{\\sqrt{n}} \\biggr)\n",
    "\\end{aligned} $$\n",
    "\n",
    "Then, the $(1 - \\alpha)100\\%$ confidence interval for the mean $\\mu$ is:\n",
    "\n",
    "$$ \\biggr[ \\bar{x} - z_{\\alpha/2} \\frac{\\sigma}{\\sqrt{n}} \\, , \\; \\bar{x} + z_{\\alpha/2} \\frac{\\sigma}{\\sqrt{n}} \\biggr] $$\n",
    "\n",
    "where $\\bar{x}$ is one realization of $\\bar{X}$.    \n",
    "Recall that confidence intervals are random variables, and can have different values for different samples!\n",
    "\n",
    "Usually it is common to calculate the $95\\%$ confidence interval.     \n",
    "For a $95\\%$ confidence interval, $1-\\alpha = 0.95$, so that $\\alpha/2 = 0.025$, and $z_{0.025} = 1.96$.\n",
    "\n",
    "Let $X_i \\sim \\mathcal{N}(\\mu,\\sigma^2)$. **Let us assume $\\sigma$ is unknown**.\n",
    "\n",
    "We can consider instead the [sample variance](https://en.wikipedia.org/wiki/Variance#Sample_variance) (unbiased version, $\\mathbb{E}[S^2] = \\sigma^2$):\n",
    "\n",
    "$$ S^2 = \\frac{1}{n-1} \\sum_{i=1}^{n} (X_i - \\bar{X})^2 $$\n",
    "and the statistics\n",
    "$$ T = \\frac{\\bar{X} - \\mu}{\\frac{S}{\\sqrt{n}}} $$\n",
    "\n",
    "Let us recall that:\n",
    "- $\\bar{X}$ and $S^2$ are independent.\n",
    "- $S^2 \\sim \\frac{\\sigma^2}{n-1} \\chi^2_{n-1}.$\n",
    "- $T \\sim t_{n-1}$ (**student t distribution**) [wiki]().\n",
    "\n",
    "Following the same steps as above, we can compute the **t-confidence interval for the mean**:\n",
    "\n",
    "$$ \\biggr[ \\bar{x} - t_{\\alpha/2,n-1} \\frac{s}{\\sqrt{n}} \\, , \\; \\bar{x} + t_{\\alpha/2,n-1} \\frac{s}{\\sqrt{n}} \\biggr] $$\n",
    "\n",
    "where $\\bar{x}$ and $s$ are realizations of $\\bar{X}$ and $S$.    \n",
    "For $T \\sim t_{n-1}$, we call $t_{\\alpha/2,n-1}$ the value such that: \n",
    "\n",
    "$$ \\mathbb{P}(T< -t_{\\alpha/2,n-1}) = \\mathbb{P}(T > t_{\\alpha/2,n-1}) = \\alpha/2. $$\n",
    "\n",
    "Recall that the student t density is symmetric.     \n",
    "The term $\\frac{s}{\\sqrt{n}}$ is called **standard error** for the mean.\n",
    "\n",
    "##### Non-normal data\n",
    "\n",
    "Thanks to the central limit theorem, the ratio $\\frac{\\bar{X} - \\mu}{\\frac{\\sigma}{\\sqrt{n}}}$ approaches a standard normal distribution for $n$ big enough.  In general $n>30$ is enough.    \n",
    "\n",
    "For big $n$ the values of $t_{\\alpha/2,n-1}$ and $z_{\\alpha/2}$ are very close. Therefore they are interchangeable.\n",
    "\n",
    "#### Confidence intervals for the variance\n",
    "\n",
    "The Chi-square distribution is asymmetric, therefore we define $a = \\chi^2_{1-\\alpha/2,n-1}$ and $b = \\chi^2_{\\alpha/2,n-1}$ and write:\n",
    "\n",
    "\\begin{align*}\n",
    "(1 - \\alpha) &= \\mathbb{P} \\biggl( a < \\frac{(n-1) S^2}{\\sigma^2} < b \\biggr) \\\\\n",
    "             &= \\mathbb{P} \\biggl( \\frac{(n-1) S^2}{b} <  \\sigma^2 < \\frac{(n-1) S^2}{a} \\biggr)\n",
    "\\end{align*}\n",
    "\n",
    "The confidence interval for the variance is therefore:\n",
    "\n",
    "$$ \\biggl[ \\frac{(n-1) S^2}{b} \\, , \\, \\frac{(n-1) S^2}{a} \\biggr] .$$\n",
    "\n",
    "For the standard deviation $\\sigma$, the confidence interval is:\n",
    "\n",
    "$$ \\biggl[ \\sqrt{\\frac{(n-1) S^2}{b}} \\, , \\, \\sqrt{\\frac{(n-1) S^2}{a}} \\biggr] .$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### A step back\n",
    "Ok... cool... a lot of theory.     \n",
    "Let's see how it works in practice for the terminal value of the Brownian motion $X_T$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The expectation of the mean is: 9.982654\n",
      "The confidence interval is:  (9.920766648111108, 10.044541975623869)\n"
     ]
    }
   ],
   "source": [
    "print(\"The expectation of the mean is: {:.6f}\".format(X_end.mean()) )\n",
    "print(\"The confidence interval is: \", ss.t.interval(0.95, paths-1, loc=X_end.mean(), scale=ss.sem(X_end)) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The estimated Standard Deviation is: 1.996432\n",
      "The confidence interval is:  1.9536249339404514 2.041170826805831\n"
     ]
    }
   ],
   "source": [
    "s2 = X_end.var(ddof=1)   # unbiased sample variance\n",
    "AA = s2 * (paths-1) \n",
    "print(\"The estimated Standard Deviation is: {:.6f}\".format(X_end.std(ddof=1)) )\n",
    "print(\"The confidence interval is: \", \\\n",
    "      np.sqrt(AA / ss.chi2.ppf(0.975, df=paths-1)), np.sqrt(AA / ss.chi2.ppf(0.025, df=paths-1)) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Sometimes the confidence interval fails!\n",
    "\n",
    "We chose a $95\\%$ confidence interval. This means that $5\\%$ of the times it fails!\n",
    "\n",
    "In the following cell, I want to check how many times the confidence interval fails to contain the population mean (in this case it is $\\mu T = 10$), if we repeat the experiment 100 times. For this purpose we just need to change the seed of the random number generator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed: 23 \n",
      " 10.0 is not contained in  (9.8494, 9.9735)\n",
      "seed: 68 \n",
      " 10.0 is not contained in  (9.875, 9.9985)\n",
      "seed: 99 \n",
      " 10.0 is not contained in  (10.0291, 10.1555)\n"
     ]
    }
   ],
   "source": [
    "for n in range(100):\n",
    "    np.random.seed(seed=n)\n",
    "    XT = ss.norm.rvs(loc=mu*T, scale=np.sqrt(T)*sig, size=paths)\n",
    "    low = ss.t.interval(0.95, paths-1, loc=XT.mean(), scale=ss.sem(XT))[0]\n",
    "    high = ss.t.interval(0.95, paths-1, loc=XT.mean(), scale=ss.sem(XT))[1]\n",
    "    if (mu*T < low) or (mu*T > high):\n",
    "        print(\"seed:\", n, '\\n', mu*T, \"is not contained in \", (low.round(4),high.round(4)) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Well... it failed 3 times!!**\n",
    "\n",
    "The parameters can be estimated by the following `scipy.stats` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters from the fit:  (9.982654311867488, 1.9961824533945993)\n",
      "The MLE estimator for the standard deviation is:  1.9961824533945993\n"
     ]
    }
   ],
   "source": [
    "param = ss.norm.fit(X_end)\n",
    "print(\"Parameters from the fit: \", param) # these are MLE parameters\n",
    "print(\"The MLE estimator for the standard deviation is: \", np.std(X_end, ddof=0) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(X_end.min(), X_end.max(), 100)\n",
    "pdf_fitted = ss.norm.pdf(x, *param)\n",
    "\n",
    "plt.plot(x, pdf_fitted, color='r', label=\"Normal\")\n",
    "plt.hist(X_end, density=True, bins=50, facecolor=\"LightBlue\", label=\"frequency of X_end\")\n",
    "plt.legend(); plt.title(\"Histogram vs Normal distribution\"); plt.xlabel(\"X_end\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1.3'></a>\n",
    "## Hypothesis testing\n",
    "\n",
    "Hypothesis testing is a broad topic. It is hard to summarize it here.    \n",
    "A summaru of the topic can be found here [statistical hypothesis testing](https://en.wikipedia.org/wiki/Statistical_hypothesis_testing). The two fundamental concepts to understand are: the [Test Statistic](https://en.wikipedia.org/wiki/Test_statistic)\n",
    "and the [p-value](https://en.wikipedia.org/wiki/P-value). \n",
    "\n",
    "For what concerns practical applications, only the **p-value** is necessary. \n",
    "It is the probability of obtaining values of the test statistic more extreme than those observed in the data, assuming the null hypothesis $H_0$ being true.     \n",
    "The p-value is the smallest significance level $\\alpha$ that leads us to rejecting the null hypothesis.\n",
    "\n",
    "Here I want to use some \"classical tests\" for testing the normality of $X_T$. \n",
    "- **Shapiro-Wilk**, [doc](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.shapiro.html)      \n",
    "  The null hypothesis $H_0$ is that the data are normally distributed.    \n",
    "  It returns the test statistics and the p-value.\n",
    "- **Jarque-Bera** [doc](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.jarque_bera.html)     \n",
    "  The null hypothesis $H_0$ is that the data are normally distributed.    \n",
    "  It returns the test statistics and the p-value. \n",
    "- **Kolmogorov-Smirnov**, [doc](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.kstest.html)    \n",
    "  It compares two distributions.     \n",
    "  The null hypothesis $H_0$ assumes the two distributions identical.\n",
    "\n",
    "Other common tests are: The [Anderson-Darling](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anderson.html#scipy.stats.anderson) test and the [D'Agostino](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.normaltest.html) test.\n",
    "\n",
    "It is also quite useful to visualize the **Q-Q plot**.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Shapiro - Wilk:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9995095729827881, 0.41248953342437744)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss.shapiro(X_end)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming a confidence level of $95\\%$. Since the p-value is not smaller that 0.05, we cannot reject $H_0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Jarque - Bera:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.8821352125475588, 0.39021102116709205)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss.jarque_bera(X_end)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming a confidence level of $95\\%$. Since the p-value is not smaller that 0.05, we cannot reject $H_0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Kolmogorov - Smirnov:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KstestResult(statistic=0.010299978780936525, pvalue=0.7897982616019145)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss.kstest(X_end, lambda x: ss.norm.cdf(x,loc=10, scale=2) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming a confidence level of $95\\%$. Since the p-value is not smaller that 0.05, we cannot reject $H_0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Q-Q plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqplot(X_end, line='s');  plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2'></a>\n",
    "# Geometric Brownian Motion\n",
    "\n",
    "The GBM has the following stochastic differential equation (SDE):\n",
    "\n",
    "$$ dS_t = \\mu S_t dt + \\sigma S_t dW_t $$\n",
    "\n",
    "By applying the Itô lemma on $\\log S_t$ it is possible to solve this equation (see the computations [here](https://en.wikipedia.org/wiki/Geometric_Brownian_motion)).     \n",
    "The solution is:\n",
    "\n",
    "$$ S_t = S_0 e^{(\\mu-\\frac{1}{2}\\sigma^2)t + \\sigma W_t} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=42) \n",
    "mu = 0.1\n",
    "sig = 0.2\n",
    "T = 10\n",
    "N = 10000 \n",
    "S0 = 1\n",
    "\n",
    "W = ss.norm.rvs( loc=(mu - 0.5 * sig**2)*T, scale=np.sqrt(T)*sig, size=N )\n",
    "S_T = S0 * np.exp(W)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we consider a lognormal random variable $S \\sim LN(\\mu, \\sigma^2)$,\n",
    "the two parameters $\\mu$ and $\\sigma$ are not the location and scale parameters of the lognormal distribution.    \n",
    "They are respectively the location and scale parameters of the normally distributed $\\ln S \\sim \\mathcal{N}(\\mu,\\sigma^2)$.    \n",
    "\n",
    "Using our specific notation $S \\sim LN(\\mu -\\frac{1}{2}\\sigma^2, \\sigma^2)$, the scale parameter is $e^{(\\mu-\\frac{1}{2}\\sigma^2)T }$ and the shape parameter is $\\sigma \\sqrt{T}$.    \n",
    "The location is zero, because the distribution starts at zero. (changing the $loc$ parameter would shift the support of the distribution on the domain $[loc,\\infty]$ )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitted parameters:  (0.6335031590210367, -0.0031793067974526315, 2.226428161130303)\n",
      "Shape:  0.632455532033676\n",
      "Scale:  2.225540928492468\n"
     ]
    }
   ],
   "source": [
    "param_LN = ss.lognorm.fit(S_T)\n",
    "print(\"Fitted parameters: \", param_LN)\n",
    "print(\"Shape: \", sig*np.sqrt(T) )\n",
    "print(\"Scale: \", np.exp((mu - 0.5 * sig**2)*T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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TgcCMiV0TJkzgiy++iHQYxk/81ugPHIDiYiqyjjhs1g9HD3Ie2IfVGOMB8Zvov/8eoN5EX969J2RkWKI3xnhC/Cb6HTsAqMjqevi8hATIzbVEb4zxBEv09fToARg2DFavdmr1xhgTw+L3x1hfos9sJNE//jhs2QJ9+4YvLmOasDB/R1DXd97AbkFdn4k+8d2jF6GyS2b984cNc+6tfGMMjzzyCMcccwyXXHJJpEMJucrKSk455RSGDx/Oiy++eMi8c845h2effbb2+bXXXssf//jHkMUyadIkgnFOUXz36I84Ak1q4CUYMsQZtviLL2DatPDGZkyUefzxx3nrrbcOuyB1VVUVSQ39DcWozz//nIMHD9Y7VMMjjzzCiSeeyNlnn826dev49NNPDxmjJ1rFd4++WyNfWdPTISfHevQm7s2aNYtNmzZxzjnn8OCDDzJnzhxmzpzJaaedxuWXX051dTX/+Z//yXHHHUdubi7z5s0DnIHJbrzxRgYNGsSZZ57JGWecwSuvvAJAdnY2u3btAiAvL49JkyYBUFZWxtVXX81xxx3HscceW3tG7dNPP815553H5MmTycnJ4Re/+EVtfG+//TYjRoxg2LBhnHzyydTU1JCTk4Pv2tM1NTX079+/dns+u3fv5txzzyU3N5exY8eyevVqCgsLufTSS1m1ahXDhw9n48aNhyyTnZ3NzJkz+cUvfsH111/Pn/70J5KTkxt87VauXMkJJ5zAyJEjOf3009nhlownTZrEHXfcwejRoxkwYEDtyJz79+9n+vTp5ObmcvHFF7N///4WvWd1eetfcXM0lejBKd+EaVx8Y6LV3Llzefvtt/nggw/IzMxkzpw5rFy5kmXLltGmTRvmz59Phw4dWLFiBZWVlYwfP57TTjuNzz//nPz8fL788kt27tzJoEGDuPrqqxvd1j333MNJJ53EggUL+OGHHxg9ejSnnHIK4Ix4+fnnn5OamsrAgQO56aabSEtL49prr2Xp0qX06dOH3bt3k5CQwKWXXsrzzz/PrbfeynvvvcewYcPIzDy0TPub3/yGY489ltdee43333+fyy+/nFWrVvHkk09y33338cYbb9Qb4+23306/fv2YMGECEyfWewlswBka+aabbuL1118nKyuLF198kTvvvLP2TOGqqio+++wzlixZwt133817773HE088Qdu2bVm9ejWrV69mxIgRzXmrGhTfiX748MbbDBsGL7/sjGTZvn144jImBpxzzjm0adMGgHfffZfVq1fX9tb37t3L+vXrWbp0KTNmzCAxMZGjjjqKk046qcn1vvvuuyxevJj77rsPgIqKitorV5188sm1A6QNGjSIrVu3smfPHiZOnFhbUurcuTPgXLlq6tSp3HrrrSxYsICrrrrqsG0tW7asdpTNk046ieLiYvbu3dtkjKtXr0ZV+frrr6mpqSEhof7CSH5+PmvWrOHUU08FoLq6mm5+ncvzzjsPgJEjR9aOm7906VJuvvlmAHJzc8nNzW0ynkDEZ6KvroadOwPr0YNzmKU7BKsx5tAx4VWVRx99lNNPP/2QNkuWLGlwjPqkpKTa671WVFQcsq5XX32VgQMHHtL+008/rR1nHiAxMZGqqipUtd5t9OzZk65du/L+++/z6aef8vzzzx/Wpr4BHZsaU7+mpobrr7+eZ599lrlz5/LEE09www031NtWVRk8eDDLly+vd75vf3z7EmgMLRGfib6oyDk+3hK9iUHRdjjk6aefzhNPPMFJJ51EcnIy33zzDd27d2fixInMmzePyy+/nMLCQj744IPaK05lZ2ezcuVKpkyZUtur9q3r0Ucf5dFHH0VE+PzzzxsdnnjcuHHccMMNbN68ubZ04+vVX3PNNVx66aVcdtllJCYmHrbsxIkTef7557nrrrv48MMPyczMpH0T39znzZtHTk4OkyZNYsCAAYwbN46LLrqIrKysw9oOHDiQoqIili9fzrhx4zh48CDffPMNgwcPbnD9vphOPPFE1qxZw+rVqxuNJ1Dx+WOs+4NIk4m+Rw/o1Ml+kDWmEddccw2DBg1ixIgRDBkyhJ/97GdUVVUxbdo0cnJyGDp0KNdddx0nnHBC7TK/+c1vuOWWW5gwYcIhSfiuu+7i4MGD5ObmMmTIEO66665Gt52VlcX8+fM577zzGDZsGBdffHHtvHPOOYfS0tJ6yzbgXLM2Ly+P3NxcZs+ezTPPPNPotgoLC7n33ntry0pHHXUUt9xyyyE/DPtLSUnhlVde4Y477mDYsGEMHz68yYuSX3fddZSWlpKbm8sf/vAHRo8e3Wj7QMXnePRLlsCZZ8LHH7Owc3a9TWp7TSeeCPv3wyefhC4eYxoRa+PRN+TKK6/krLPO4oILLgjL9vLy8rjttttqj2jxkpBcHFxEJotIvohsEJHZ9cyfKiKrRWSViOSJyE8CXTYiAujRL8zfwcL8HWzo1Z+q1atZuK4g6GckGmNC4/e//z3nn38+v/vd7yIdSlRoskYvIonAY8CpQAGwQkQWq6r/ZdT/CSxWVRWRXOAl4OgAlw0/X6I/8kjYuqfRpnsHHE3S/v203V5Aec/eYQjOGG96+umnw7at2bNnM3t2+PqV06ZNY/PmzYdMu/feew/7gTpSAvkxdjSwQVU3AYjIC8BUoDZZq2qpX/t0QANdNiJ27HBq7wFcCb60Tz8AMjZvtERvIqaho0tMdFgUxmtMt6TcHkjppjuwze95gTvtECIyTUS+Bt4Erm7Osu7yM92yT57vjLaQCeRkKVdJn/4AZGzaEMqIjGlQWloaxcXFLfoDN96iqhQXF5MWQCfVXyA9+vq6EYd94lR1EbBIRCYCvwVOCXRZd/n5wHxwfowNIK6Wa0aiP9CpMwc6dKTd5o1NNzYmBHr06EFBQQEh7wCZmJCWlkaPHj2abugnkERfAPT0e94D2N5QY1VdKiL9RCSzucuGzY4dMGFCYG1FKMnuR4YlehMhycnJhw0mZkxzBFK6WQHkiEgfEUkBpgOL/RuISH9xC4giMgJIAYoDWTbsVJvVowco7dvPevTGmJjVZKJX1SrgRuAd4CvgJVVdKyKzRGSW2+x8YI2IrMI5yuZiddS7bCh2JGB79jgXBm9Goi/p0482RTtJKi0JYWDGGBMaAQ2BoKpLgCV1ps31e3wvcG+gy0ZUoGfF+il1f5Btt3kTjBwQiqiMMSZk4m8IhBYk+hLfIZZbrHxjjIk98Zfov//euW9Goi/r1ZuaxEQ7xNIYE5PiL9G3oEdfk5JKeY9e9oOsMSYmxWeiT0+HjIxmLVaSbUfeGGNiU3wm+mb05n1K+/Sj3dZNzjj2xhgTQ+Iv0RcWQteuzV6spE8/kioqYNu2phsbY0wUib9E38Lrv5b0dQ6xJD8/yAEZY0xoxV+iLylpdn0efhzFkq+/DnJAxhgTWvGX6Pfta1Gir+ySyYGM9tajN8bEnPhL9C3s0SPi9Oot0RtjYkx8JfqaGigtbVmixz1D1hK9MSbGxFeiLytz7luY6Ev79IeCgh/XY4wxMSCgQc28YGH+DtJ2fs8ZwOflNWxuwYW+fWPe8M03cOyxwQ3QGGNCJK569EllzqVtq9LbtWj50uy+zoNvvglWSMYYE3JxluidksvBlib63tkgYnV6Y0xMibNE37oefU1aG+jVy3r0xpiYEleJPrm8dYkegAEDLNEbY2JKXCV6X+mmKj295SsZONAp3agGKSpjjAmtOEv0QerR79vnDI5mjDExIC4TfUt/jAWcRA9WvjHGxIy4SvTJpaWoCNVt27Z8JQMHOvd25I0xJkYElOhFZLKI5IvIBhGZXc/8S0RktXv7WESG+c3bIiJfisgqEckLZvDNlVRWSlXbdOcQyZbq2RNSU61Hb4yJGU2eGSsiicBjwKlAAbBCRBar6jq/ZpuBE1R1j4hMAeYDY/zmn6iqu4IYd4sklZW2rj4PkJgIOTnWozfGxIxAevSjgQ2quklVDwAvAFP9G6jqx6q6x336CdAjuGEGR1JZWeuOuPGxQyyNMTEkkETfHfC/fl6BO60h/wG85fdcgXdFZKWIzGxoIRGZKSJ5IpJXVFQUQFjNF5QePTiJfuNGqKpq/bqMMSbEAkn09RW06z2IXEROxEn0d/hNHq+qI4ApwA0iMrG+ZVV1vqqOUtVRWVlZAYTVfEllpa074sZn4EA4eBC2bGn9uowxJsQCSfQFQE+/5z2A7XUbiUgu8CQwVVWLfdNVdbt7XwgswikFRURQSzdg5RtjTEwIJNGvAHJEpI+IpADTgcX+DUSkF7AQuExVv/Gbni4iGb7HwGnAmmAF31zJZaVUtWvZWPSH8CV6+0HWGBMDmjzqRlWrRORG4B0gEVigqmtFZJY7fy7wa6AL8Lg4hy5WqeoooCuwyJ2WBPxVVd8OyZ4EIGg1+sxM6NzZevTGmJgQ0IVHVHUJsKTOtLl+j68BrqlnuU3AsLrTIyWprIyDwSjdgB15Y4yJGXFzZqwcPEjigcrg9Ojhx8HNjDEmysXNpQSDMqAZziUJAQZ26sbg777j9X9voDo9nfMGdmt1jMYYEwpx06NPLvUl+uCUbkrcywq227opKOszxphQiZtEH6wevU9p3/4AZGzaEJT1GWNMqFiib6HS7D5oQgIZm9YHZX3GGBMqcZTofRcGD07ppiYllbKevcnYtDEo6zPGmFCJo0Qf3B49QEnf/mRstB69MSa6xU2iTw5Bot/XL4d2WzYhNriZMSaKxU2i/7FHH6QTpoDSPv1JPHiAtt9ta7qxMcZESPwk+nKnRh/sHj1g5RtjTFSLn0RfVkp1cgo1KalBW+ePh1haojfGRK+4SvTBLNsAHGzfgYqsI+xYemNMVIujRF8W1LKNz76+OWRstERvjIlecZPok4M1RHEdpX37O6UbrfeiW8YYE3Fxk+hDUboB2Ne3Pykl+2DnzqCv2xhjgiF+En1paHr0Je6RN3z1VdDXbYwxwRA/iT5YFwavw3fkjSV6Y0y0iptEnxysC4PXsb9rNw62TYevvw76uo0xJhjiJtEH7XqxdYk4vXrr0RtjolR8JHpVkspDc3gluGfIWqI3xkSp+Ej05eVITU1ISjcAJX1z4LvvoKQkJOs3xpjWCCjRi8hkEckXkQ0iMrue+ZeIyGr39rGIDAt02bBwE3CoevS1P8hand4YE4WaTPQikgg8BkwBBgEzRGRQnWabgRNUNRf4LTC/GcuGnpvoQ3HUDfw4uBlr14Zk/cYY0xqB9OhHAxtUdZOqHgBeAKb6N1DVj1V1j/v0E6BHoMuGRW2PPjSlm9LefSAtDb78MiTrN8aY1ggk0XcH/AdcL3CnNeQ/gLeau6yIzBSRPBHJKyoqCiCsZvAl+nYZwV2vT2IiDBpkid4YE5UCSfRSz7R6B3YRkRNxEv0dzV1WVeer6ihVHZWVlRVAWM0Q4ho9AEOHWqI3xkSlQBJ9AdDT73kPYHvdRiKSCzwJTFXV4uYsG3K1NfrQlG4AJ9F//z3s2hW6bRhjTAsEkuhXADki0kdEUoDpwGL/BiLSC1gIXKaq3zRn2bDYtw8IQ48erFdvjIk6TSZ6Va0CbgTeAb4CXlLVtSIyS0Rmuc1+DXQBHheRVSKS19iyIdiPxoWrdAOW6I0xUScpkEaqugRYUmfaXL/H1wDXBLps2PkSfdsQlm6OPBK6dIE1a0K3DWOMaYH4ODO2pISqtm0hIYS7K2I/yBpjolL8JPpQlm18hg51evQ1NaHfljHGBChuEv3BtmFK9KWlsHVr6LdljDEBiptEH6qzYg9hP8gaY6JQHCX6MPToBw927i3RG2OiSBwl+jD06DMyoE8fS/TGmKgS0OGVMa+sjKqjeod0EwvzdwAwLrs/6Ss/5z33+XkDu4V0u8YY05T46NGXlVHdtm1YNrV3wDG027yRhAOVYdmeMcY0JW4SfVVam7Bsat+Ao0moriZj04awbM8YY5oSN4m+uk2YevQDneuqtM+3a8gaY6KD9xP9gQNQVeWcGRsGpdl9qUpLo+M6+0HWGBMdvJ/oy8oAwtaj16Qk9h49mE5rV4dle8YY05S4SfRVYUr0AD8MzqXDOhsKwRgTHeIm0YfrqBuAPYNzSS4vo92WjWHbpjHGNCRuEn1Vm/AcdQNOjx6g0w8K0zcAABRWSURBVFqr0xtjIi9uEn24avQAJf1ynB9k11id3hgTeXGT6MNZo9ekJPYOHExH+0HWGBMF4ibRh7NGD/DD4KF0/Mp+kDXGRJ73E315ORDeHj04dfrkslJYvz6s2zXGmLq8n+gjUKMH2DPE+UGWlSvDul1jjKkrbhJ9uM6M9SnpN4Dq1DRL9MaYiAso0YvIZBHJF5ENIjK7nvlHi8hyEakUkdvrzNsiIl+KyCoRyQtW4AHz9ejDNKiZj3OG7CBL9MaYiGtyPHoRSQQeA04FCoAVIrJYVdf5NdsN3Ayc28BqTlTVXa0NtkXKyiAlBU0K/9D7ewYPpfPfFzo/yCZ4/8uTMSY6BZJ9RgMbVHWTqh4AXgCm+jdQ1UJVXQEcDEGMrVNWBuG4ulQ9fhicCyUl9oOsMSaiAkn03YFtfs8L3GmBUuBdEVkpIjMbaiQiM0UkT0TyioqKmrH6JkQw0e8ZMsx5YOUbY0wEBZLopZ5p2oxtjFfVEcAU4AYRmVhfI1Wdr6qjVHVUVlZWM1bfhAgm+pJ+A6BtW/jkk4hs3xhjILBEXwD09HveA9ge6AZUdbt7XwgswikFhU8EE70mJcGYMfCvf0Vk+8YYA4El+hVAjoj0EZEUYDqwOJCVi0i6iGT4HgOnAWtaGmyLRDDRAzB+PHzxBZSWRi4GY0xca/JQFFWtEpEbgXeARGCBqq4VkVnu/LkiciSQB7QHakTkVmAQkAksEhHftv6qqm+HZlcaUFYGmZlh3eQhxo+H6mr49FM4+eTIxWGMiVsBHXOoqkuAJXWmzfV7/D1OSaeufcCw1gTYamVl0Lt35LY/bhyIOOUbS/TGmAjw/sHdkS7ddOgAQ4ZYnd4YEzGW6MNh/HhYvtwp4RhjTJhZog+H8eOdE6fWhPd3aGOMAa8n+poaqKiIjkQPVr4xxkSEtxO9OxZ9xBN9djZ062aJ3hgTEd5O9O7IlYR5iOLDiDi9ekv0xpgIiI9EH+kePTiJfutW+O67SEdijIkzluhDbGH+Dhbm7+CD7gMA+PTlN1iYvyNi8Rhj4o8l+jD54ZghVLVpQ+aK5ZEOxRgTZyzRh4kmJ7PruHEc8fFHkQ7FGBNnLNGHUeHxE8nYsok22wsiHYoxJo5Yog+jwuOdofiP+HhphCMxxsQTS/RhtC9nIBVZR1j5xhgTVpbow0mEwnETOGL5R85Zu8YYEwaW6MOs8PiJpO7Z7VyMxBhjwsD7iT4hAVJTIx1JrcJxE5wH//hHZAMxxsQN7yf69HRnCIIoUdH1SPbmDLREb4wJG28n+vLyqCrb+BQePxE++gj27490KMaYOODtRB8NY9HXo/D4iVBZCcuWRToUY0wc8H6ij/TIlfXYNWosJCfDu+9GOhRjTBzwfqKPwh59dXo6nHACvP46qEY6HGOMxwWU6EVksojki8gGEZldz/yjRWS5iFSKyO3NWTakojTRAzBtGqxfD199FelIjDEe12SiF5FE4DFgCjAImCEig+o02w3cDNzXgmVDJ5oT/dSpzv2iRZGNwxjjeYH06EcDG1R1k6oeAF4Apvo3UNVCVV0BHGzusiEVzYm+e3cYM8YSvTEm5AJJ9N2BbX7PC9xpgQh4WRGZKSJ5IpJXVFQU4OqbEM2JHpzyzcqV8O23kY7EGONhgST6+s42CvQXxICXVdX5qjpKVUdlZWUFuPomxEKiB3jttcjGYYzxtEASfQHQ0+95D2B7gOtvzbKtoxr9iX7AABg0yMo3xpiQCiTRrwByRKSPiKQA04HFAa6/Ncu2TmWlM0JkNCd6cHr1S5fCrl2RjsQY41FNJnpVrQJuBN4BvgJeUtW1IjJLRGYBiMiRIlIA/Bz4LxEpEJH2DS0bqp05RBSOXFmvadOcf0h//3ukIzHGeFRSII1UdQmwpM60uX6Pv8cpywS0bFjESqIfMQJ69YKXX4arrop0NMYYDwoo0cekKE/0C/N31D4ePHkqA558jLc+WsUZE4ZHMCpjjBd5dwiEKE/0/raeeyFSU0PPv78a6VCMMR7k3URfXu7cx0CiL+3bn+LhI+n12ss29o0xJui8m+h9PfooHL2yPt+eexEd1uc7J1AZY0wQeT/Rx0CPHqDgjHOoTkmFp5+OdCjGGI+xRB8lDrbvwPZTJsPf/uacA2CMMUFiiT6KfDvtIti9G954I9KhGGM8xBJ9FNl5/EQ46ih46qlIh2KM8RDvJ/oY+TEWgMREuPZaeOstyM+PdDTGGI/wdqJPS3OSZyy57jpISYGHH450JMYYj/B2oo+hsk2trl3hkkvgmWecer0xxrSS5xL9wvwdLMzfwdbtuyhPTat9HlNuu8054Wv+/EhHYozxAM8lep+k/eVUtYmh+ry/oUPhlFPg0UfhwIFIR2OMiXGeTfSJ+8upjsFE7/sG8q8Lr4Dt21nxyJ9j81uJMSZqeDbRx3SPHtg54URK+vQj56nHnfHqjTGmhTyb6BPLy6mOpUMr60pI4OtZt9Dx63V0f/fNSEdjjIlh3k30FfupSmsT6TBaZdtZ09jXfwCDHv4DUlUV6XCMMTHKs4k+qbwstnv0AImJrLvlDjI2b6TX669EOhpjTIzyZqJXJXX3bio7dY50JK22/ZTJ7B46nGMeu98GOzPGtIgnE31SWSmJByqp7JIV6VBaT4S1t82m7fbvYN68SEdjjIlBnkz0qcW7AKjskhnhSIKjaNwECseMh9/+FoqLIx2OMSbGBJToRWSyiOSLyAYRmV3PfBGRR9z5q0VkhN+8LSLypYisEpG8YAbfkNTiIsA7iR4RVv/qbtizB+64I9LRGGNiTJOJXkQSgceAKcAgYIaIDKrTbAqQ495mAk/UmX+iqg5X1VGtD7lpaW6vt8IriR7YN3CQMzTCU0/BRx9FOhxjTAwJpEc/GtigqptU9QDwAjC1TpupwP+q4xOgo4h0C3KsAfNa6abWnDnQqxfMmmVDIxhjAhZIou8ObPN7XuBOC7SNAu+KyEoRmdnQRkRkpojkiUheUVFRAGE1rLZ006lLq9YTddLT4bHHYN06uP/+SEdjjIkRgSR6qWeaNqPNeFUdgVPeuUFEJta3EVWdr6qjVHVUVlbrjpZJLd7FgQ4d0ZSUVq0n2izM38HCnJF8d+oZVM+5m/cW/9PGwDHGNCmQRF8A9PR73gPYHmgbVfXdFwKLcEpBIZW6u5jKzh7rzftZNef3HOzQgdG3zSKxvDzS4RhjolwgiX4FkCMifUQkBZgOLK7TZjFwuXv0zVhgr6ruEJF0EckAEJF04DRgTRDjr1fqriLv1ef9VHbJZMUfHiVj80aG//ZXkQ7HGBPlmkz0qloF3Ai8A3wFvKSqa0VklojMcpstATYBG4A/A9e707sCy0TkC+Az4E1VfTvI+3CY1N27qPDCyVKNKBo3gfxZt9B70Uvw3HORDscYE8WSAmmkqktwkrn/tLl+jxW4oZ7lNgHDWhljs6UWF1M51rulG5+vbvg5mZ99TOasWTBkCAwfHumQjDFRyHNnxsrBg6Tu3UNlZ++Wbnw0KYnPHpgLnTvDmWfCtm1NL2SMiTueS/Spu52Tpbxco/dX0fVIWLIESkvhjDNg795Ih2SMiTIeTPS+k6W8XaM/xJAhsHAhfP01nH8+VFREOiJjTBTxXqKvPSvW+zV6n4X5O1jYYxAr7nkA/vlPdp4ymddXbYx0WMaYKOHdRB8HNfq6tk29gLz/eZAjPl7K8T+73CnnGGPiXkBH3cQSX6KvyIyj0o2fb8+7mJqUFEbdcTPFEyax/IlnOFDnAiznDYzYMETGmAjwXo9+9y6qk1OoapcR6VAipuCsaXz24Dw6rv2SSRedSftvvo50SMaYCPJcok/btcupz0t9w+/Ej+2nncHSZ18lqWI/J0w/m27vvxPpkIwxEeK5RJ+6e1d8HXHTiD3DR/L+K29R2rc/466/iiH33k1CpR2RY0y88V6iL94VN8fQB6Kiazf+77mFbJp+OQP+Mo8TLzgDvvgi0mEZY8LIg4m+KC6PuGlMTVobVs35Pf+a9yype4rhuOPgzjuhrCzSoRljwsBbiV6V1OJiKjIt0ddn5wkn897f34eLLoL/+R84+mh48UXQupcXMMZ4ibcS/b59JB48YD36Rhzo1MUZ7fKjjyAzE6ZPhzFjnGEULOEb40neSvQ7dwLxM85Nq/zkJ5CXB08+CUVFzqBoY8c6QylUVUU6OmNMEHnrhKnCQsASfVMOufzgT85AFp9C79dfZsRTjzlj5fTqBddfD1dfDa28rKMxJvK81aO3RN8impLClgsvgQ0bYNEi6NcPZs+Go46Cs8+Gl1+G/fsjHaYxpoW81aP3lW6sRt8iCzcUwjFj4InnyVifT6/XX6bX4oW0eeMNaNsWJk+Gc8+FKVOc+r4xJiZ4s0fv4QuDh0tJzkDW3v5fvPXBCvjHP+CKK+CTT+Dyy+GII2DkSKfX/847sG9fpMM1xjTCWz36wkIqO3RCk5MjHYl3JCaysOdguGUw3HQnndauputHH3DEx0vpfP/9JNx7LyrC3gHHsHv4SH4YnMuIM09yxshPSYl09MYYQDQKD6kbNWqU5uXlNX/BCy9k379X8d6SpcEPyhwmsayMzl+spMu/V9Dl3yvo9OUqUkrc3n1SEgwY4CT8QYOcxwMGQE4OtG8f2cCN8SARWamqo+qb560e/c6dNs5NGFWnp1N0/ESKjp/oTFAlfdtWOq5dTYev19F+Qz7tP/mM9JdfRvw7FJ07Q58+kJ0NPXs6tx49oFs3OPJI59auXdwPTGdMsASU6EVkMvAwkAg8qaq/rzNf3PlnAOXAlar670CWDarCQir7DAjZ6k0TRCjrlU1Zr2y+m3JO7eSEygrSv91KxpZNpG/dRHrBNtp+t422n39B27feIqm8/PB1paU5vwVkZUGXLj/eOnWCjh2dW4cOzq19e8jIcP45ZGRAejpY+c6YWk0mehFJBB4DTgUKgBUislhV1/k1mwLkuLcxwBPAmACXDZ7CQipHjgvJqk3L1aSmUZIzkJKcgYfPVCW5ZB9tvt9BWtFO0ooKSSvaScruYgZU73d+YN+9GzZuhOJi5+LnAZQba5KTqWrTluo2balKa0NGxwxo08b5B+K7T0398T4l5cd7/1ty8uG3pKTDb4mJP943dktI+PHe91jkx+d1b755Ij/e/J/7PzamAYH06EcDG1R1E4CIvABMBfyT9VTgf9Up+H8iIh1FpBuQHcCywaEKM2awa8CwoK/ahJAIB9t34GD7DuwbcPQhs9bU176mhqSyUlL27iWprITk0hKSS0pIKislqbyMpLIyksrLSNxfTlJ5OYkV+0msqKDEvU8orSCx+AcSKytJOFBJ4oFKEg4ccG+VJB44gNTUhGXXQ8L/H0JDN/92LXlcd1u+x/7TW/q47vqb06Y584LdJljLZmbCp5+2fHsNCCTRdwe2+T0vwOm1N9Wme4DLAiAiM4GZ7tNSEckPIDZ/mYBzHUF+1sxFY4bfPnpaPOxnaPZRNdrGLLL3sjk2bWrNP5beDc0IJNHXt9W6n6SG2gSyrDNRdT4wP4B46iUieQ394uwV8bCPEB/7GQ/7CPGxn7Gwj4Ek+gKgp9/zHsD2ANukBLCsMcaYEArkzNgVQI6I9BGRFGA6sLhOm8XA5eIYC+xV1R0BLmuMMSaEmuzRq2qViNwIvINziOQCVV0rIrPc+XOBJTiHVm7AObzyqsaWDcmetKLsE0PiYR8hPvYzHvYR4mM/o34fo/LMWGOMMcHjrUHNjDHGHMYSvTHGeFzMJ3oRmSwi+SKyQURmRzqeUBGRLSLypYisEpEWjPgWfURkgYgUisgav2mdReQfIrLeve8UyRiDoYH9nCMi37nv5yoROSOSMbaWiPQUkQ9E5CsRWSsit7jTPfN+NrKPUf9exnSN3h1i4Rv8hlgAZoRsiIUIEpEtwChV9czJJyIyESjFOat6iDvtD8BuVf29+4+7k6reEck4W6uB/ZwDlKrqfZGMLVjcM+G7qeq/RSQDWAmcC1yJR97PRvbxIqL8vYz1Hn3t8AyqegDwDbFgYoCqLgV215k8FXjGffwMzh9STGtgPz1FVXf4BjJU1RLgK5wz4z3zfjayj1Ev1hN9Q0MveJEC74rISne4CK/q6p6DgXt/RITjCaUbRWS1W9qJ2ZJGXSKSDRwLfIpH3886+whR/l7GeqIPeIgFDxivqiNwRgq9wS0HmNj1BNAPGA7sAO6PbDjBISLtgFeBW1XVk9eYrGcfo/69jPVEH8jwDJ6gqtvd+0JgEU7Zyot2urVQX020MMLxhISq7lTValWtAf6MB95PEUnGSYDPq+pCd7Kn3s/69jEW3stYT/RxMcSCiKS7P/4gIunAaTQwiq8HLAaucB9fAbwewVhCxpf8XNOI8ffTvfjQU8BXqvqA3yzPvJ8N7WMsvJcxfdQNgHso00P8OMTCPREOKehEpC9OLx6cYSv+6oX9FJG/AZNwhnndCfwGeA14CegFfAtcqKox/UNmA/s5CeervgJbgJ/5atmxSER+AnwEfAn4BvT/FU4N2xPvZyP7OIMofy9jPtEbY4xpXKyXbowxxjTBEr0xxnicJXpjjPE4S/TGGONxluiNMcbjLNEbY4zHWaI3pg4RudMdhna1O+zsmHraLHLnbRCRvX5D1B4fiZiNaYwdR2+MHxEZBzwATFLVShHJBFJ8Q1DU034ScLuqnhXGMI1pliYvDm5MnOkG7FLVSgAvjf9v4peVbow51LtATxH5RkQeF5ETIh2QMa1lid4YP6paCowEZgJFwIsicmVEgzKmlax0Y0wdqloNfAh8KCJf4oy6+HQkYzKmNaxHb4wfERkoIjl+k4YDWyMVjzHBYD16Yw7VDnhURDoCVcAGnDKOMTHLDq80xhiPs9KNMcZ4nJVujGmCiCwC+tSZfIeqvhOJeIxpLivdGGOMx1npxhhjPM4SvTHGeJwlemOM8ThL9MYY43H/H7VOFSBXaIsiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(S_T.min(), S_T.max(), 100)\n",
    "pdf_LN_fitted = ss.lognorm.pdf(x, *param_LN)\n",
    "\n",
    "plt.plot(x, pdf_LN_fitted, color='r', label=\"Log-Normal\")\n",
    "plt.hist(S_T, density=True, bins=50, facecolor=\"LightBlue\", label=\"frequency of X_end\")\n",
    "plt.legend(); plt.title(\"Histogram vs Log-Normal distribution\"); plt.xlabel(\"S_T\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Parameter estimation:\n",
    "\n",
    "In order to estimate the parameters, we need to take first the logarithm of the data!\n",
    "\n",
    "The variable of interest is\n",
    "$$\\log S_T \\sim \\mathcal{N} \\biggl( (\\mu-\\frac{1}{2}\\sigma^2)T, \\sigma^2 T \\biggr)$$\n",
    "\n",
    "Now we can estimate the mean and the variance of a Normal distributed sample. This is quite easy!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Volatility or coefficient sig:  0.200682\n",
      "Drift or coefficient mu:  0.100002\n"
     ]
    }
   ],
   "source": [
    "std_S = np.std(np.log(S_T), ddof=0 )/np.sqrt(T)\n",
    "mu_S = np.mean(np.log(S_T))/T + 0.5 * std_S**2\n",
    "\n",
    "print(\"Volatility or coefficient sig: \", std_S.round(6))\n",
    "print(\"Drift or coefficient mu: \", mu_S.round(6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Path simulation\n",
    "\n",
    "There is no need to use advanced techniques.     \n",
    "\n",
    "If we want to simulate GBM paths, it is enough to simulate Brownian paths (with the adjusted drift) and then take their exponentials!\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(seed=42) \n",
    "paths=10              # number of paths\n",
    "steps=1000            # number of time steps\n",
    "T = 10                \n",
    "T_vec, dt = np.linspace(0, T, steps, retstep=True)\n",
    "\n",
    "X0 = np.zeros((paths,1))        # each path starts at zero\n",
    "W = ss.norm.rvs( (mu - 0.5 * sig**2)*dt, np.sqrt(dt)*sig, (paths,steps-1))\n",
    "X = np.concatenate((X0,W), axis=1).cumsum(1)\n",
    "\n",
    "S_T = np.exp(X)\n",
    "plt.plot(T_vec, S_T.T ); plt.title(\"Geometric Brownian paths\"); plt.xlabel(\"T\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3'></a>\n",
    "# CIR process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Cox-Ingersoll-Ross process [CIR](https://en.wikipedia.org/wiki/Cox%E2%80%93Ingersoll%E2%80%93Ross_model) is described by the SDE: \n",
    "\n",
    "$$ dX_t = \\kappa (\\theta - X_t) dt + \\sigma \\sqrt{X_t} dW_t $$\n",
    "\n",
    "The parameters are:\n",
    "- $\\kappa$ mean reversion coefficient\n",
    "- $\\theta$ long term mean  \n",
    "- $\\sigma$  volatility coefficient\n",
    "\n",
    "If $2\\kappa \\theta > \\sigma^2$ (Feller condition), the process is always strictly positive!\n",
    "\n",
    "**Curiosity for mathematicians**     \n",
    "The diffusion coefficient of the CIR equation does not satisfy the Lipschitz conditions (square root is not Lipschitz)!!  However, it can be proved that the CIR equation admits a unique solution. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I recall a common technique used to solve SDEs numerically. [wiki](https://en.wikipedia.org/wiki/Euler%E2%80%93Maruyama_method)\n",
    "\n",
    "<a id='sec3.1'></a>\n",
    "## Euler Maruyama method\n",
    "\n",
    "Let us divide the time interval $[0,T]$ in \n",
    "$$0=t_0, t_1, ..., t_{n-1}, t_n=T.$$      \n",
    "We can choose equally spaced points $t_i$ such that $\\Delta t = t_{i+1} - t_i = \\frac{T}{N}$ for each $1 \\leq i \\leq N$.\n",
    "\n",
    "A generic Itô-Diffusion SDE\n",
    "\n",
    "\\begin{align*}\n",
    "&dX_t = \\mu(t,X_t) dt + \\sigma(t, X_t) dW_t \\\\\n",
    "&X_0 = 0\n",
    "\\end{align*}\n",
    "\n",
    "can be approximated by:\n",
    "\n",
    "\\begin{align*}\n",
    "& X_{i+1} = X_i + \\mu(t_i,X_i) \\Delta t + \\sigma(t_i, X_i) \\Delta W_i \\\\\n",
    "&X_0 = 0\n",
    "\\end{align*}\n",
    "\n",
    "with $X(t_i) = X_i$ and $W(t_i) = W_i$.     \n",
    "The quantity to simulate is $W_{i+1} - W_i = \\Delta W_i \\sim \\mathcal{N}(0, \\sqrt{\\Delta t})$.\n",
    "\n",
    "Applying this method to the CIR SDE we obtain:\n",
    "\n",
    "$$ X_{i+1} = X_i + \\kappa (\\theta - X_i) \\Delta t + \\sigma \\sqrt{X_i} \\Delta W_i $$\n",
    "\n",
    "Despite the presence of the Feller condition, when we discretize the process, it is possible that $X_i$ becomes negative, creating problems in the evaluation of the square root.    \n",
    "Here I summarize the most common methods to overcome this problem:\n",
    "\n",
    "1) $ X_{i+1} = X_i + \\kappa (\\theta - X_i) \\Delta t + \\sigma \\sqrt{X_i^+} \\Delta W_i $\n",
    "\n",
    "2) $ X_{i+1} = X_i + \\kappa (\\theta - X_i^+) \\Delta t + \\sigma \\sqrt{X_i^+} \\Delta W_i $\n",
    "\n",
    "3) $ X_{i+1} = X_i + \\kappa (\\theta - X_i) \\Delta t + \\sigma \\sqrt{|X_i|} \\Delta W_i $\n",
    "\n",
    "4) $ X_{i+1} = |X_i + \\kappa (\\theta - X_i) \\Delta t + \\sigma \\sqrt{X_i} \\Delta W_i |$\n",
    "\n",
    "where ^+ indicates the positive part.     \n",
    "The methods 1) 2) and 3) just resolve the square root problem, but the process can still become negative.   \n",
    "The method 4) prevents this possibility!\n",
    "\n",
    "Let us have a look at the implementation of the **method 4)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 41.9 s, sys: 3.08 s, total: 45 s\n",
      "Wall time: 45 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "np.random.seed(seed=42) \n",
    "\n",
    "N = 200001        # time steps \n",
    "paths = 2000      # number of paths \n",
    "T = 3\n",
    "T_vec, dt = np.linspace(0,T,N, retstep=True ) \n",
    "\n",
    "kappa = 4 \n",
    "theta = 1 \n",
    "sigma = 0.5     \n",
    "std_asy = np.sqrt( theta * sigma**2 /(2*kappa) )   # asymptotic standard deviation\n",
    "\n",
    "X0 = 2\n",
    "X = np.zeros((paths,N))\n",
    "X[:,0] = X0\n",
    "W = ss.norm.rvs( loc=0, scale=np.sqrt(dt), size=(paths,N-1) )\n",
    "\n",
    "for t in range(0,N-1):\n",
    "    X[:,t+1] = np.abs( X[:,t] + kappa*(theta - X[:,t])*dt + sigma * np.sqrt(X[:,t]) * W[:,t] )\n",
    "\n",
    "X_T = X[:,-1]    # values of X at time T\n",
    "X_1 = X[1,:]     # a single path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Feller condition is:  True\n"
     ]
    }
   ],
   "source": [
    "print(\"Feller condition is: \", 2*kappa * theta > sigma**2 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "plt.plot(T_vec, X_1, label=\"CIR process\")\n",
    "plt.plot(T_vec, (theta + std_asy)*np.ones_like(T_vec), label=\"1 asymptotic std dev\", color=\"black\" )\n",
    "plt.plot(T_vec, (theta - std_asy)*np.ones_like(T_vec), color=\"black\" )\n",
    "plt.plot(T_vec, theta*np.ones_like(T_vec), label=\"Long term mean\" )\n",
    "plt.legend(loc=\"upper right\"); plt.title(\"CIR process\"); plt.xlabel(\"T\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the plot above I also included the asymptotic mean and standard deviation:\n",
    "\n",
    "$$ \\mathbb{E}[X_T|X_0] \\underset{T\\to \\infty}{\\to} \\theta $$    \n",
    "$$ Var[X_T|X_0] \\underset{T\\to \\infty}{\\to} \\frac{\\theta \\sigma^2}{2\\kappa} $$    \n",
    "\n",
    "You can find the complete formulas [here](https://en.wikipedia.org/wiki/Cox%E2%80%93Ingersoll%E2%80%93Ross_model#Properties).\n",
    "\n",
    "Let us also recall that the conditional distribution of $X_T$ is a (scaled) non-central Chi-Squared distribution:\n",
    "\n",
    "$$ X_T \\sim \\frac{Y}{2c} $$\n",
    "\n",
    "with $c=\\frac{2\\kappa}{(1-e^{-kT})\\sigma^2}$, and the random variable $Y$ follows the non-central $\\chi^2$ distribution:\n",
    "\n",
    "$$ f\\bigl( y|x_0;\\, K,\\lambda \\bigr) = \\frac{1}{2} e^{-\\frac{(\\lambda+y)}{2} } \\biggl( \\frac{y}{\\lambda} \\biggr)^{ \\frac{K-2}{4} } I_{ \\frac{K-2}{2} } (\\sqrt{\\lambda y})  $$\n",
    "\n",
    "with $K=\\frac{4\\theta \\kappa}{\\sigma^2}$ degrees of freedom and non-centrality parameter $\\lambda = 2 c X_0 e^{-\\kappa T}$.   (`scipy.stats.ncx2` uses this parameterization, see [link](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ncx2.html))\n",
    "\n",
    "After the variable transformation, the density of $X_T$ is:\n",
    "\n",
    "$$ f(x|x_0; \\kappa,\\theta,\\sigma) = c e^{-(u+v)} \\biggl( \\frac{v}{u} \\biggr)^{q/2} I_q(2\\sqrt{uv})  $$\n",
    "\n",
    "with $q = \\frac{2\\theta \\kappa}{\\sigma^2} - 1$,  $u = c x_0 e^{-\\kappa T}$, $v = c x$. \n",
    "\n",
    "The function $I_q$ is a modified Bessel function of first kind.  See [1] for more details.\n",
    "\n",
    "The two parameterizations are related by $K=2q+2$ and $\\lambda=2u$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def CIR_pdf(x, x0, T, k, t, s):\n",
    "    \"\"\"\n",
    "    Density of the CIR process\n",
    "    x: array value\n",
    "    x0: starting point, \n",
    "    T: terminal time, \n",
    "    k,t,s: kappa, theta, sigma\n",
    "    \"\"\"\n",
    "    c = 2*k / ((1-np.exp(-k*T))*s**2)\n",
    "    q = 2*k*t / s**2 - 1\n",
    "    u = c*x0*np.exp(-k*T)  \n",
    "    v = c * x\n",
    "    \n",
    "    return c * np.exp(-u-v) * (v/u)**(q/2) * iv(q, 2*np.sqrt(u*v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3.2'></a>\n",
    "## Parameters estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### OLS\n",
    "\n",
    "We can rewrite the equation as:\n",
    "\n",
    "$$ \\frac{X_{i+1} - X_i}{\\sqrt{X_i}} = \\frac{\\kappa \\theta \\Delta t}{\\sqrt{X_i}} - \\kappa \\sqrt{X_i} \\Delta t + \\sigma \\Delta W_i. $$\n",
    "\n",
    "Now we can find the parameters by OLS. \n",
    "\n",
    "$$ (\\hat{\\kappa}, \\hat{\\theta}) = \\arg \\min_{\\kappa,\\theta} \\sum_{i=0}^{N-2} \\biggl( \\frac{X_{i+1} - X_i}{\\sqrt{X_i}} - \\frac{\\kappa \\theta \\Delta t}{\\sqrt{X_i}} + \\kappa \\sqrt{X_i} \\Delta t \\biggr)^2 $$\n",
    "\n",
    "After a lot of calculations, it is possible to find an expression for $(\\hat{\\kappa}, \\hat{\\theta})$.  I will not write it in latex (it is long), but just in python in the following cell. \n",
    "\n",
    "We call:\n",
    "- $YY = \\frac{X_{i+1} - X_i}{\\sqrt{X_i}} $.    \n",
    "- $XX_1 = \\frac{1}{\\sqrt{X_i}} $.     \n",
    "- $XX_2 = \\sqrt{X_i} $.     \n",
    "\n",
    "The parameter $\\sigma$ can be estimated from the residuals. The choice of `ddof=2` is common when estimating the standard deviation of residuals in linear regressions (it corresponds to the number of parameters already estimated).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "kappa OLS:  4.456356687802874\n",
      "theta OLS:  0.9783705727798766\n",
      "sigma OLS:  0.5003617989457074\n"
     ]
    }
   ],
   "source": [
    "# formulas for the OLS estimators kappa and theta\n",
    "num = N**2 - 2*N + 1 + sum(X_1[1:]) * sum(1/X_1[:-1]) \\\n",
    "                - sum(X_1[:-1]) * sum(1/X_1[:-1]) - (N-1) * sum(X_1[1:]/X_1[:-1])\n",
    "den = (N**2 - 2*N + 1 - sum(X_1[:-1]) * sum(1/X_1[:-1]) ) * dt\n",
    "kappa_OLS = num/den\n",
    "theta_OLS = ((N-1) * sum(X_1[1:]) - sum(X_1[1:]/X_1[:-1]) * sum(X_1[:-1]) ) / num\n",
    "\n",
    "# residuals of the regression\n",
    "YY = (X_1[1:] - X_1[:-1])/np.sqrt(X_1[:-1])   # response variable\n",
    "XX1 = 1 / np.sqrt(X_1[:-1])                   # regressor 1 \n",
    "XX2 = np.sqrt(X_1[:-1])                       # regressor 2\n",
    "sigma_OLS = np.std(YY - theta_OLS * kappa_OLS * dt * XX1 + dt * kappa_OLS * XX2, ddof=2 )/ np.sqrt(dt)\n",
    "print(\"kappa OLS: \", kappa_OLS)\n",
    "print(\"theta OLS: \", theta_OLS)\n",
    "print(\"sigma OLS: \", sigma_OLS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you are lazy... and you don't want to read, write or understand this extremely long OLS formula, you can use a solver for minimizing the sum of the squares. \n",
    "\n",
    "Here I'm using the `scipy.optimize` function [minimize](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html).\n",
    "\n",
    "There are several algorithms that work quite well. An alternative to Nelder-Mead can be the L-BFGS-B algorithm.    \n",
    "Since the variables are positive, I'm also specifying the bounds (but it helps only for L-BFGS-B).\n",
    "\n",
    "The coefficients are given in the last row. We can see that they coincide with those obtained before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/scipy/optimize/_minimize.py:516: RuntimeWarning: Method Nelder-Mead cannot handle constraints nor bounds.\n",
      "  RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       " final_simplex: (array([[4.45633236, 0.97837109],\n",
       "       [4.45633237, 0.97837109],\n",
       "       [4.45633237, 0.97837109]]), array([0.75107828, 0.75107828, 0.75107828]))\n",
       "           fun: 0.7510782789840907\n",
       "       message: 'Optimization terminated successfully.'\n",
       "          nfev: 157\n",
       "           nit: 75\n",
       "        status: 0\n",
       "       success: True\n",
       "             x: array([4.45633236, 0.97837109])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def least_sq(c):\n",
    "    return sum((YY - c[1] * c[0] * dt * XX1 + dt * c[0] * XX2)**2)\n",
    "\n",
    "minimize(least_sq, x0=[1,1], method='Nelder-Mead', bounds=[[1e-15,None],[1e-15,None]], tol=1e-8) # L-BFGS-B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, if you change the initial parameters of the simulation, the estimation procedure can give different results.\n",
    "\n",
    "I tried to change the seed, several times.    \n",
    "After some trials, I found that $\\kappa$ is the most \"volatile\" parameter, while $\\theta$ and $\\sigma$ are quite stable.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let us compare the density with the histogram of all realizations of $X_T$.\n",
    "\n",
    "We can also use the `scipy.stats.ncx2` ([doc](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ncx2.html)) class to fit the scaled Non-Central Chi-Squared density. However, the results can be very different. \n",
    "\n",
    "I will plot the density of $X_T$ under these wrong parameters, and compare it with the right density in the picture below. The two densities are very close!\n",
    "\n",
    "In practice, when we don't know the values of the original parameters, it is always better to try several calibratition techniques and then compare them!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters from the scipy fit: \n",
      " Degrees of freedom: 29.07865663614399 \n",
      " Non-Centrality: 29.497594667208162 \n",
      " Location: 0.21146560859835073 \n",
      " Scale: 0.013445207387043327 \n"
     ]
    }
   ],
   "source": [
    "param_Chi2 = ss.ncx2.fit(X_T)    # fit parameters\n",
    "print(\"Parameters from the scipy fit: \\n Degrees of freedom: {} \\n \\\n",
    "Non-Centrality: {} \\n Location: {} \\n Scale: {} \".format(*param_Chi2) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `CIR_pdf` function defined above, corresponds to the function `ss.ncx2.pdf` \n",
    "after the change of parameterization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xxx = np.linspace(0.1, 2, 100)\n",
    "\n",
    "c = 2*kappa / ((1-np.exp(-kappa*T))*sigma**2)\n",
    "q = 2*kappa*theta / sigma**2 -1\n",
    "u = c*X0*np.exp(-kappa*T) \n",
    "df = 2*q+2                       # parameter K\n",
    "nc = u*2                         # parameter lambda\n",
    "\n",
    "plt.plot(xxx, CIR_pdf(xxx, X0, T, kappa, theta, sigma), label=\"CIR_pdf\")\n",
    "plt.plot(xxx, ss.ncx2.pdf(xxx, df, nc, scale=1/(2*c)), label=\"ncx2\")\n",
    "plt.legend(); plt.title(\"same density \"); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(X_T.min(), X_T.max(), 100)\n",
    "pdf_Chi2_fitted = ss.ncx2.pdf(x, *param_Chi2)             # distribution with fitted parameters \n",
    "\n",
    "plt.figure(figsize=(14,7))\n",
    "plt.plot(x, CIR_pdf(x, X0, T, kappa, theta, sigma), label=\"original parameters\")\n",
    "plt.plot(x, CIR_pdf(x, X0, T, kappa_OLS, theta_OLS, sigma_OLS), label=\"OLS parameters\")\n",
    "plt.plot(x, pdf_Chi2_fitted, color='r', label=\"scipy fitted param\")\n",
    "plt.hist(X_T, density=True, bins=70, facecolor=\"LightBlue\", label=\"frequencies of X_T\")\n",
    "plt.legend(); plt.title(\"Histogram vs Non-Central Chi-Squared distribution\"); plt.xlabel(\"X_T\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that with `ncx2.fit(X_T)`, we fitted the distribution at time T.     \n",
    "\n",
    "**But this is not what happens in practice!!**       \n",
    "In practice, when working with financial market data, we just have 1 realized path! (we just have one realization of $X_T$).     \n",
    "Moreover, we cannot use `ncx2.fit` with the returns series, because the returns are not identically distributed.\n",
    "\n",
    "The OLS method described above is the right method to use! An alternative can be to use the MLE method, considering the conditional probability density.\n",
    "\n",
    "\n",
    "### Comment\n",
    "\n",
    "If we know the conditional density, why do we need to solve numerically the SDE?  Why can't we just generate random variables from this density?\n",
    "\n",
    "**Well, we can! And in some circumstances it is the best thing to do!**\n",
    "But the CIR process is mainly used as a model for the volatility dynamics in the Heston model, where the SDE approach is easier to implement!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3.3'></a>\n",
    "## Change of variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A nice trick to solve the problem of negative values is to change variables. (this is a recurrent trick in financial math)\n",
    "\n",
    "Let us consider the log-variable:\n",
    "\n",
    "$$  Y_t = \\log X_t $$\n",
    "\n",
    "The new variable $Y_t$ can be negative for $0<X_t<1$.\n",
    "\n",
    "By Itô lemma we obtain the evolution of $Y_t$:\n",
    "\n",
    "$$ dY_t = e^{-Y_t} \\biggl[ \\kappa (\\theta - e^{Y_t}) - \\frac{1}{2}\\sigma^2 \\biggr] dt + \\sigma e^{-2 Y_t} dW_t $$\n",
    "\n",
    "Using the Euler-Maruyama method, \n",
    "\n",
    "$$ Y_{i+1} = Y_i + e^{-Y_i} \\biggl[ \\kappa (\\theta - e^{Y_i}) - \\frac{1}{2}\\sigma^2 \\biggr] \\Delta t + \\sigma e^{-2 Y_i} \\Delta W_i $$\n",
    "\n",
    "let us simulate some paths."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=42) \n",
    "\n",
    "N = 200001        # time steps \n",
    "paths = 2         # number of paths \n",
    "T = 3\n",
    "T_vec, dt = np.linspace(0,T,N, retstep=True ) \n",
    "\n",
    "kappa = 4 \n",
    "theta = 1 \n",
    "sigma = 0.5     \n",
    "std_asy = np.sqrt( theta * sigma**2 /(2*kappa) )   # asymptotic standard deviation\n",
    "\n",
    "X0 = 2\n",
    "Y0 = np.log(X0)\n",
    "\n",
    "Y = np.zeros((paths,N))\n",
    "Y[:,0] = Y0\n",
    "W = ss.norm.rvs( loc=0, scale=np.sqrt(dt), size=(paths,N-1) )\n",
    "\n",
    "for t in range(0,N-1):\n",
    "    Y[:,t+1] = Y[:,t] + np.exp(-Y[:,t])*( kappa*(theta - np.exp(Y[:,t])) - 0.5*sigma**2 )*dt \\\n",
    "                                          + sigma * np.exp(-Y[:,t]/2) * W[:,t] \n",
    "\n",
    "Y_T = Y[:,-1]    # values of X at time T\n",
    "Y_1 = Y[1,:]     # a single path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "plt.plot(T_vec, np.exp(Y_1), label=\"CIR process\")\n",
    "plt.plot(T_vec, (theta + std_asy)*np.ones_like(T_vec), label=\"1 asymptotic std dev\", color=\"black\" )\n",
    "plt.plot(T_vec, (theta - std_asy)*np.ones_like(T_vec), color=\"black\" )\n",
    "plt.plot(T_vec, theta*np.ones_like(T_vec), label=\"Long term mean\" )\n",
    "plt.legend(loc=\"upper right\"); plt.title(\"CIR process - by log-transformation\"); plt.xlabel(\"T\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the path did not change. (under same parameters and same seed as before). \n",
    " \n",
    "**This is (in my opinion) the best theoretical approach!** \n",
    "\n",
    "However, in practice, this is not the perfect method. It can have several problems for small values of $N$.     \n",
    "For instance, as the algorithm involves an exponential function, it can generate huge numbers and even NaNs.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1]  Cox, J.C., Ingersoll, J.E and Ross, S.A. A Theory of the Term Structure of Interest Rates.\n",
    "Econometrica, Vol. 53, No. 2 (March, 1985)"
   ]
  }
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